If labor and capital both exhibit increasing marginal products, then a production function cannot exhibit diminishing marginal rate of technical substitution of labor for capital.
a. True
b. False
The correct answer is (b.) False
Even if the production function exhibits increasing marginal products, then also it can have a diminishing marginal rate of technical substitution, as marginal rate of technical substitution is
and is independent of the fact whether they are increasing or not.
If labor and capital both exhibit increasing marginal products, then a production function cannot exhibit diminishing...
You might think that when a production function has a diminishing marginal rate of technical substitution of labor for capital, it cannot have increasing marginal products of capital and labor. Show that this is not true, using the production function Q = L2K2.
The production function q = k0.620.5 exhibits: a. increasing returns to scale and diminishing marginal products for both k and 1. b. increasing returns to scale and diminishing marginal product for 1 only. c. increasing returns to scale but no diminishing marginal productivities. d. decreasing returns to scale.
For each of the following production functions, solve for the marginal products of each input and marginal rate of substitution. Then answer the following for each: does this production function exhibit diminishing marginal product of labour? Does this production function exhibit diminishing marginal product of capital? Does this production function exhibit constant, decreasing, or increasing returns to scale? Show all your work.(a) \(Q=L+K\)(b) \(Q=2 L^{2}+K^{2}\)(c) \(Q=L^{1 / 2} K^{1 / 2}\)
The production function 9 = k1.270.5 exhibits: a. increasing returns to scale but no diminishing marginal productivities. b. decreasing returns to scale. C. increasing returns to scale and diminishing marginal product for / only. d. increasing returns to scale and diminishing marginal products for both k and I.
4. Consider the production functions given below: a. Suppose that the production function faced by a milk producer is given by Q = 40.5 20.5 = 4VK VL, where MPx = 2K-0.5 20.5 = 2 and MP, = 2 K0.5L-05 = 2 * i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS = 1) iii. Does this production function display...
For each production function below, find the marginal product of capital and labor, and the marginal rate of technical substitution. Show whether the production function exhibits CRS DRS, or IRS. For parts a and b, draw what the isoquant looks like for 10 units of output (a) f(K, L) 2K + 2L (b) f(K, L) 2K1/4L/4 (c) f(K, L) K1/2 L/2
For a production function with a diminishing, but positive, marginal product of labor: A. Output increases at an increasing rate as more workers are employed B. Output increases at a decreasing rate as more workers are employed. C. Output declines as more workers are employed. D. The effects on marginal product are unknown.
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
Here we have the production function y=f(K,L)=K3L, where K is capital input and L is labor input. Let K>0, L>0. 1. What are the marginal products of capital and labor re- spectively? 2. Please compute the technical rate of substitution (we as- sume K is on the horizontal axis). 3. Dose this production function show diminishing technical rate of substitution (in absolute value) when K increases? Please give a brief proof. 4. Please prove that this production function features increas-...
Consider the production function given by y = f(L,K) = L^(1/2) K^(1/3) , where y is the output, L is the labour input, and K is the capital input. (a) Does this exhibit constant, increasing, or decreasing returns to scale? (b) Suppose that the firm employs 9 units of capital, and in the short-run, it cannot change this amount. Then what is the short-run production function? (c) Determine whether the short-run production function exhibits diminishing marginal product of labour. (d)...